Continuity results for parametric nonlinear singular Dirichlet problems

Advances in Nonlinear Analysis

article

Yunru Bai¹  Dumitru Motreanu²  Shengda Zeng¹ 

[1] Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science;Département de Mathématiques, Université de Perpignan

关键词: Parametric singular elliptic equation;    p-Laplacian;    smallest solution;    sequential continuity;    monotonicity;   

DOI  :  10.1515/anona-2020-0005

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper we study from a qualitative point of view the nonlinear singular Dirichlet problem depending on a parameter λ > 0 that was considered in [32]. Denoting by S λ the set of positive solutions of the problem corresponding to the parameter λ , we establish the following essential properties of S λ : there exists a smallest element uλ∗ $\begin{array}{} u_\lambda^* \end{array}$ in S λ , and the mapping λ ↦ uλ∗ $\begin{array}{} u_\lambda^* \end{array}$ is (strictly) increasing and left continuous; the set-valued mapping λ ↦ S λ is sequentially continuous.

【 授权许可】

CC BY